求出最大的積

利用 A.M. >= G.M.

[a(1) + a(2) + ... + a(n)]/n >= [a(1)a(2)...a(n)]^(1/n)

現在 a(1) + a(2) + ... + a(n) = 30

30/n >= [a(1)a(2)...a(n)]^(1/n)

a(1)a(2)...a(n) <= (30/n)^n

容易發現達最大值時a(1) = a(2) = ... = a(n)。例如：

n = 1,最大值 = 30

n = 2,最大值 = 225

n = 3,最大值 = 1000

希望幫到你

計到的數字是有限大無限細
0.1^x>0.01^x

Anyway, what is the greatest product.
The question like : Find the greatest area of a polygon if the area is equal to
3*x^2 - 4x -5.
You cannot tell me that it depends on x, when x is smaller, the area becomes smaller. And said that the question does not specify the range of area.

2011-12-29 14:37:30 補充：
Bingo, your answer is correct. But why don't you post it as myisland8132 not give me the answer.
Due to typo error, you are right, the question of the example is to find the min area.

2011-12-30 10:14:11 補充：
According to myisland8132, you should using differentiation to find maximum n.
As the result is 11.036, so n is 11.
Anyway, you said you haven't learnt AM>=GM, then what is your level now?

發問者,你並沒有講出n是多少,範圍也沒有
myisland8132 ( 知識長 )已經計了,
最大的積depends on n
n=1,姐係30
n=2,就係15,15,姐係225
n=4,就係7.5,7.5,7.5,7.5,姐係3164.0625
明唔明,有幾多n,最大積就係
(30/n)^n

2011-12-29 12:25:17 補充：
我並沒有說n 越大時積越大,我只是說最大的積depends on n

2011-12-29 12:41:38 補充：
我唔知你條題目係唔係有問題,不過3x^2 - 4x -5只能計出 the min. area
而(30/n)^n when n係正整數,最大既積係n=11, 62088.94

2011-12-29 21:39:04 補充：
說真的,我並未學到用A.M. >= G.M. 所以就不回答了

這條數 myisland8132 ( 知識長 ) 都算是最佳回答了

P.S. 11呢個答案我是用pascal計的,不太算數學 @@

2011-12-30 12:09:32 補充：
F.4 = ="